Simulation results for a study of the relationship between predicting species distributions and the suitability of habitat.

Loading in data…some sims are skipped because they didn’t produce viable distributions to sample from. These will be rerun eventually.

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Summary statistics

method cor.all.spearman cor.native.spearman cor.all.pearson cor.native.pearson cor.all.hoslem cor.native.hoslem train.auc test.auc train.max.tss test.max.tss train.max.kappa test.max.kappa
bc 0.3043371 0.2355392 0.3421751 0.2355735 170012.45 87202.09 0.7089074 0.6523858 0.4391202 0.3363781 0.1992323 0.1916576
brt 0.1030779 0.2530662 0.2761195 0.2303648 127581.66 67773.34 0.8775116 0.7490646 0.6350337 0.4784065 0.4978000 0.3186590
dm 0.5180400 0.2098033 0.5843531 0.2135364 80600.59 42003.46 0.6441629 0.6254632 0.2775001 0.3043340 0.1605659 0.1793822
gam 0.3485121 0.1714372 0.1973356 0.1358000 193139.56 86831.72 0.8641932 0.7224554 0.6162773 0.4466814 0.4452006 0.2887339
glm 0.1856778 0.2588919 0.0703818 0.2185764 244947.76 87818.71 0.7736123 0.7028037 0.4637471 0.4095257 0.3015731 0.2664851
mx 0.3966182 0.2703469 0.4962945 0.2828200 84807.10 48858.81 0.8115005 0.7323970 0.5181879 0.4518322 0.3486820 0.2923078
rf -0.1427181 0.0626064 0.0330461 0.0513677 157799.02 87586.96 0.9889538 0.7264974 0.9590988 0.4575120 0.8333636 0.3864464





Relationship between training and test AUC

This plot illustrates the relationship between a model’s ability to predict the data that was used to construct that model vs. its ability to predict a random subset of data that was witheld from the model during fitting. This basically shows what you’d expect, and what you’d hope would be true: that a model that predicts its training data well is generally better at predicting the randomly withheld test data.

## 
## Call:
## lm(formula = test.auc ~ train.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41855 -0.05928  0.01106  0.06975  0.20709 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.23594    0.01544   15.28   <2e-16 ***
## train.auc    0.57479    0.01884   30.50   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09679 on 1498 degrees of freedom
## Multiple R-squared:  0.3831, Adjusted R-squared:  0.3827 
## F-statistic: 930.5 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 0.7240088 0 0.6452058
brt 0.3878892 0 0.4123920
dm 0.6819091 0 0.6227610
gam 0.4456828 0 0.4880493
glm 0.5110205 0 0.5946948
mx 0.4579689 0 0.6269793
rf -0.0307403 0 0.1296183




Performance of models

Spearman

Examining performance of models using Spearman correlation coefficient

## [1] "Proportion of models positively correlated with true habitat suitability, native range, Spearman rank correlation:  0.73"
## [1] "Proportion of models positively correlated with true habitat suitability, continental scale, Spearman rank correlation:  0.760666666666667"
## [1] "Proportion of models positively correlated with true habitat suitability, both native range and continental scale, Spearman rank correlation:  0.609333333333333"





Relationship between Spearman rank correlation in the training region and at the continental scale

This plot and regression demonstrate the relationship between the ability to predict the relative suitability of habitat within the training region and the ability of the model to extrapolate to the continental scale. The clustering of points around the 1:1 line is due to the set of species that occupy all suitable habitat, i.e., the training region and the continental extent are the same. The second plot and regression have those simulations removed.

## 
## Call:
## lm(formula = cor.all.spearman ~ cor.native.spearman, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.23903 -0.22049  0.03853  0.24126  0.82966 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          0.16606    0.01070   15.52   <2e-16 ***
## cor.native.spearman  0.39022    0.02797   13.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3476 on 1498 degrees of freedom
## Multiple R-squared:  0.115,  Adjusted R-squared:  0.1144 
## F-statistic: 194.6 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 0.3915081 0.0000000 0.3956701
brt 0.3449451 0.0000025 0.1102667
dm 0.2878832 0.0000000 0.1721463
gam 0.2599580 0.0010083 0.0489348
glm 0.2251982 0.0089553 0.0312042
mx 0.3106005 0.0000012 0.1038302
rf 0.5131796 0.0000000 0.2232413
## 
## 
## 
##  Same plot and regression, with 1:1 simulations removed

## 
## Call:
## lm(formula = cor.all.spearman ~ cor.native.spearman, data = new.table[new.table$occupancy < 
##     1, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.22015 -0.23283  0.04343  0.25440  0.78304 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          0.18573    0.01164   15.95   <2e-16 ***
## cor.native.spearman  0.31956    0.03048   10.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3587 on 1353 degrees of freedom
## Multiple R-squared:  0.07513,    Adjusted R-squared:  0.07445 
## F-statistic: 109.9 on 1 and 1353 DF,  p-value: < 2.2e-16
coef p r.sq
bc 0.3541692 0.0000000 0.3503571
brt 0.3003841 0.0001225 0.0828943
dm 0.2725324 0.0000000 0.1595079
gam 0.1774843 0.0350389 0.0225855
glm 0.1557348 0.0946511 0.0142594
mx 0.2367083 0.0003764 0.0629478
rf 0.5072009 0.0000000 0.1969817




Density plot of Spearman rank correlation between predicted and true habitat suitability, training region only

This plot shows the distribution of Spearman rank correlations between the true relative suitability of habitat and that inferred by each model within the training region. Colors correspond to modeling algorithms.





Density plot of Spearman rank correlation between predicted and true habitat suitability, continental scale

This plot shows the distribution of Spearman rank correlations between the true relative suitability of habitat and that inferred by each model when models are projected to a continental scale. Colors correspond to modeling algorithms.





Density plots of traditional model quality metrics

These plots show the distribution of metrics for AUC, TSS, and kappa on train and test data





Relationships between traditional model quality metrics

These plots show the relationships between AUC, TSS, and kappa on randomly withheld data.

## 
## Call:
## lm(formula = test.max.kappa ~ test.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.21239 -0.05653 -0.01180  0.04484  0.38798 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.42605    0.01195  -35.66   <2e-16 ***
## test.auc     0.99906    0.01679   59.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.08011 on 1498 degrees of freedom
## Multiple R-squared:  0.7026, Adjusted R-squared:  0.7024 
## F-statistic:  3539 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 0.9371482 0 0.7987521
brt 1.0508540 0 0.7238484
dm 0.8697910 0 0.7933622
gam 0.9869672 0 0.7195675
glm 1.0189027 0 0.7523109
mx 1.0025411 0 0.7328574
rf 0.8084206 0 0.4679838

## 
## Call:
## lm(formula = test.max.tss ~ test.auc, data = new.table)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.110990 -0.035348 -0.006096  0.030946  0.176186 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.610331   0.007323  -83.34   <2e-16 ***
## test.auc     1.457389   0.010293  141.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0491 on 1498 degrees of freedom
## Multiple R-squared:  0.9305, Adjusted R-squared:  0.9304 
## F-statistic: 2.005e+04 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 1.472060 0 0.9383372
brt 1.546032 0 0.9202154
dm 1.283888 0 0.9278046
gam 1.525689 0 0.9275985
glm 1.484698 0 0.9319617
mx 1.563136 0 0.9466412
rf 1.377484 0 0.8845796

## 
## Call:
## lm(formula = test.max.tss ~ test.max.kappa, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.28713 -0.06988 -0.00405  0.06552  0.37769 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.117450   0.005447   21.56   <2e-16 ***
## test.max.kappa 1.070959   0.017521   61.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09961 on 1498 degrees of freedom
## Multiple R-squared:  0.7138, Adjusted R-squared:  0.7136 
## F-statistic:  3736 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 1.3029769 0 0.8083246
brt 1.0846325 0 0.6909632
dm 1.2125668 0 0.7891727
gam 1.1546873 0 0.7192677
glm 1.1166548 0 0.7274908
mx 1.1549751 0 0.7087974
rf 0.9297115 0 0.5627356




Relationship between test AUC and Spearman rank correlation, training region only

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat within the training region. The lack of correlation indicates that test AUC is not a good predictor of the model’s ability to estimate the relative suitability of habitat, which is very problematic.

## 
## Call:
## lm(formula = cor.native.spearman ~ test.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.09399 -0.22716  0.02415  0.23776  0.73311 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.14800    0.04786   3.092  0.00202 **
## test.auc     0.08569    0.06727   1.274  0.20292   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3209 on 1498 degrees of freedom
## Multiple R-squared:  0.001082,   Adjusted R-squared:  0.0004152 
## F-statistic: 1.623 on 1 and 1498 DF,  p-value: 0.2029
coef p r.sq
bc -0.5233939 0.0011834 0.0476262
brt 0.6659859 0.0015746 0.0513475
dm -0.8518564 0.0000163 0.0826125
gam 0.0266830 0.8767671 0.0001116
glm 0.6220245 0.0003082 0.0586268
mx 0.7106432 0.0003714 0.0571007
rf 0.6284545 0.0002650 0.0598629




Relationship between test AUC and Spearman rank correlation, continental scale

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat at a continental scale, where model transferability is an issue. The lack of correlation indicates that test AUC is not a good predictor of model transferability. In fact the (not statistically significant) effect of test AUC on model accuracy is in fact negative.

## 
## Call:
## lm(formula = cor.all.spearman ~ test.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.10221 -0.23524  0.04887  0.27383  0.70545 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.37516    0.05501   6.819 1.32e-11 ***
## test.auc    -0.18253    0.07732  -2.361   0.0184 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3688 on 1498 degrees of freedom
## Multiple R-squared:  0.003706,   Adjusted R-squared:  0.003041 
## F-statistic: 5.573 on 1 and 1498 DF,  p-value: 0.01837
coef p r.sq
bc -0.4846691 0.0000010 0.1054220
brt 0.4790017 0.0297610 0.0246155
dm 0.0068238 0.9611482 0.0000110
gam 0.5456748 0.0064947 0.0337899
glm -0.2424256 0.2765367 0.0054793
mx 0.6342492 0.0010060 0.0489528
rf 0.2782864 0.1421057 0.0099502




Relationship between test max TSS and Spearman rank correlation

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of the True Skill Statistic. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of TSS), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.spearman ~ test.max.tss, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.10708 -0.22742  0.02544  0.24000  0.72415 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.19969    0.02010   9.937   <2e-16 ***
## test.max.tss  0.02034    0.04455   0.457    0.648    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.321 on 1498 degrees of freedom
## Multiple R-squared:  0.0001392,  Adjusted R-squared:  -0.0005283 
## F-statistic: 0.2085 on 1 and 1498 DF,  p-value: 0.648
coef p r.sq
bc -0.3127249 0.0033025 0.0392650
brt 0.4213802 0.0012613 0.0533931
dm -0.7119542 0.0000014 0.1025214
gam -0.0757383 0.4854089 0.0022559
glm 0.3524387 0.0017322 0.0445171
mx 0.3606235 0.0038817 0.0379537
rf 0.3514133 0.0029618 0.0401497

## 
## Call:
## lm(formula = cor.all.spearman ~ test.max.tss, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1077 -0.2370  0.0484  0.2736  0.7135 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.30998    0.02306  13.442  < 2e-16 ***
## test.max.tss -0.15265    0.05112  -2.986  0.00287 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3684 on 1498 degrees of freedom
## Multiple R-squared:  0.005917,   Adjusted R-squared:  0.005253 
## F-statistic: 8.916 on 1 and 1498 DF,  p-value: 0.002873
coef p r.sq
bc -0.3299040 0.0000004 0.1127997
brt 0.2446686 0.0741874 0.0166816
dm -0.0644461 0.5395610 0.0017449
gam 0.2646883 0.0371636 0.0199508
glm -0.1641416 0.2571248 0.0059413
mx 0.3480075 0.0038405 0.0380402
rf 0.1894939 0.1431953 0.0098963




Relationship between test max kappa and Spearman rank correlation

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of Cohen’s kappa. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of kappa), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.spearman ~ test.max.kappa, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.14297 -0.22408  0.01945  0.23833  0.70961 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.25569    0.01750  14.610  < 2e-16 ***
## test.max.kappa -0.17387    0.05629  -3.089  0.00205 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.32 on 1498 degrees of freedom
## Multiple R-squared:  0.006328,   Adjusted R-squared:  0.005665 
## F-statistic:  9.54 on 1 and 1498 DF,  p-value: 0.002048
coef p r.sq
bc -0.6010685 0.0000860 0.0690623
brt 0.2134270 0.2160077 0.0080450
dm -0.9696937 0.0000015 0.1020799
gam -0.0529252 0.7204116 0.0005942
glm 0.3317303 0.0251044 0.0230102
mx 0.3794972 0.0273707 0.0223326
rf 0.0089054 0.9520391 0.0000168

## 
## Call:
## lm(formula = cor.all.spearman ~ test.max.kappa, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.14732 -0.23620  0.04346  0.26088  0.75231 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.38970    0.01977  19.712  < 2e-16 ***
## test.max.kappa -0.51980    0.06359  -8.174 6.27e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3615 on 1498 degrees of freedom
## Multiple R-squared:  0.0427, Adjusted R-squared:  0.04206 
## F-statistic: 66.82 on 1 and 1498 DF,  p-value: 6.275e-16
coef p r.sq
bc -0.5387415 0.0000000 0.1432207
brt 0.1485466 0.4076529 0.0036116
dm -0.1764434 0.2178942 0.0070202
gam 0.3320503 0.0550221 0.0169380
glm -0.3257679 0.0852079 0.0136537
mx 0.2979042 0.0729330 0.0148114
rf 0.1066456 0.5070174 0.0020407




Relationship between bias strength and Spearman rank correlation, training region only

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.spearman ~ bias.strength, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1238 -0.2253  0.0204  0.2353  0.7361 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.22197    0.01550  14.317   <2e-16 ***
## bias.strength -0.02769    0.02607  -1.062    0.288    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3209 on 1498 degrees of freedom
## Multiple R-squared:  0.0007527,  Adjusted R-squared:  8.567e-05 
## F-statistic: 1.128 on 1 and 1498 DF,  p-value: 0.2883
coef p r.sq
bc -0.0012466 0.9839170 0.0000019
brt -0.0800899 0.2562990 0.0067771
dm 0.0634523 0.4283876 0.0029062
gam -0.0748017 0.2342651 0.0065436
glm -0.0524343 0.4120192 0.0031179
mx -0.0448274 0.5357327 0.0017780
rf -0.0147171 0.8080144 0.0002739




Relationship between proportion of suitable habitat that falls within species range and Spearman rank correlation, training region only

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.spearman ~ occupancy, data = new.table[new.table$method != 
##     "rf", ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.14197 -0.22797  0.02571  0.24212  0.68899 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.28506    0.02459  11.592   <2e-16 ***
## occupancy   -0.09472    0.04150  -2.282   0.0226 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.32 on 1280 degrees of freedom
## Multiple R-squared:  0.004053,   Adjusted R-squared:  0.003275 
## F-statistic: 5.209 on 1 and 1280 DF,  p-value: 0.02263
coef p r.sq
bc 0.0075895 0.9340359 0.0000318
brt -0.1337044 0.1874144 0.0091286
dm -0.0016163 0.9891524 0.0000009
gam -0.0287642 0.7580792 0.0004401
glm -0.2119707 0.0245763 0.0231771
mx -0.2025782 0.0581649 0.0165161
rf -0.3449580 0.0000926 0.0684575




Rank correlation vs. bias strength and proportion of suitable habitat within range, training region only

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.native.spearman ~ bias.strength * occupancy, 
##     data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13635 -0.22568  0.01772  0.23137  0.76126 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              0.39617    0.04225   9.377  < 2e-16 ***
## bias.strength           -0.23139    0.07109  -3.255  0.00116 ** 
## occupancy               -0.31778    0.07187  -4.422 1.05e-05 ***
## bias.strength:occupancy  0.37333    0.12133   3.077  0.00213 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3189 on 1496 degrees of freedom
## Multiple R-squared:  0.01466,    Adjusted R-squared:  0.01269 
## F-statistic:  7.42 on 3 and 1496 DF,  p-value: 6.21e-05





Relationship between bias strength and Spearman rank correlation, continental scale

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.spearman ~ bias.strength, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13096 -0.23261  0.04509  0.27682  0.70467 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.27002    0.01784   15.14   <2e-16 ***
## bias.strength -0.04530    0.02999   -1.51    0.131    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3692 on 1498 degrees of freedom
## Multiple R-squared:  0.00152,    Adjusted R-squared:  0.0008539 
## F-statistic: 2.281 on 1 and 1498 DF,  p-value: 0.1312
coef p r.sq
bc 0.0174500 0.6502194 0.0009537
brt -0.1124109 0.1245471 0.0123723
dm 0.0587055 0.2906952 0.0051671
gam -0.0377946 0.6095438 0.0012097
glm -0.1270324 0.1182486 0.0112603
mx -0.0678401 0.3305991 0.0043827
rf -0.0388487 0.5546889 0.0016181




Relationship between proportion of suitable habitat that falls within species range and Spearman rank correlation, continental scale

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.spearman ~ occupancy, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.12928 -0.23141  0.04823  0.27467  0.68277 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.27481    0.02625  10.468   <2e-16 ***
## occupancy   -0.04994    0.04431  -1.127     0.26    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3694 on 1498 degrees of freedom
## Multiple R-squared:  0.0008471,  Adjusted R-squared:  0.0001801 
## F-statistic:  1.27 on 1 and 1498 DF,  p-value: 0.26
coef p r.sq
bc 0.1025540 0.0712786 0.0149832
brt 0.1105772 0.2943397 0.0057861
dm 0.0487699 0.5542058 0.0016220
gam 0.0291160 0.7907826 0.0003265
glm -0.1498566 0.2143942 0.0071276
mx -0.1663268 0.1070025 0.0119830
rf -0.3108052 0.0012609 0.0471087




Rank correlation vs. bias strength and proportion of suitable habitat within range, continental scale

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.all.spearman ~ bias.strength * occupancy, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13460 -0.23143  0.04714  0.27514  0.70411 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              0.33196    0.04892   6.786 1.65e-11 ***
## bias.strength           -0.11388    0.08231  -1.384    0.167    
## occupancy               -0.11294    0.08320  -1.357    0.175    
## bias.strength:occupancy  0.12569    0.14046   0.895    0.371    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3692 on 1496 degrees of freedom
## Multiple R-squared:  0.002901,   Adjusted R-squared:  0.000901 
## F-statistic: 1.451 on 3 and 1496 DF,  p-value: 0.2264





Relationship between Spearman rank correlation and size of the species’ range, training region only

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.spearman ~ true.breadth, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.92638 -0.20835  0.02498  0.22518  0.86238 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3.224e-01  1.220e-02   26.42   <2e-16 ***
## true.breadth -1.432e-05  1.164e-06  -12.29   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.306 on 1498 degrees of freedom
## Multiple R-squared:  0.09167,    Adjusted R-squared:  0.09106 
## F-statistic: 151.2 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -7.50e-06 0.0083717 0.0317456
brt -2.73e-05 0.0000000 0.3141001
dm 4.30e-06 0.2459889 0.0062262
gam -1.28e-05 0.0000071 0.0893131
glm -1.81e-05 0.0000000 0.1714303
mx -2.43e-05 0.0000000 0.2423078
rf -1.69e-05 0.0000000 0.1672930




Relationship between Spearman rank correlation and size of the species’ range, continental scale

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.spearman ~ true.breadth, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.15155 -0.22340  0.03713  0.28082  0.71690 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.961e-01  1.464e-02  20.223  < 2e-16 ***
## true.breadth -6.116e-06  1.397e-06  -4.377 1.29e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3672 on 1498 degrees of freedom
## Multiple R-squared:  0.01263,    Adjusted R-squared:  0.01197 
## F-statistic: 19.16 on 1 and 1498 DF,  p-value: 1.286e-05
coef p r.sq
bc -5.00e-07 0.7693467 0.0003989
brt -1.46e-05 0.0000476 0.0835960
dm -4.80e-06 0.0647243 0.0157081
gam -9.10e-06 0.0078895 0.0322227
glm 5.00e-07 0.8978642 0.0000765
mx -1.72e-05 0.0000000 0.1305917
rf -1.60e-06 0.5914071 0.0013362




Relationship between test AUC and Pearson correlation, training region only

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat within the training region. The lack of correlation indicates that test AUC is not a good predictor of the model’s ability to estimate the relative suitability of habitat, which is very problematic.

## 
## Call:
## lm(formula = cor.native.pearson ~ test.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.96945 -0.19778 -0.00791  0.19447  0.69123 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.14432    0.04225   3.416 0.000653 ***
## test.auc     0.07208    0.05938   1.214 0.225044    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2833 on 1498 degrees of freedom
## Multiple R-squared:  0.0009824,  Adjusted R-squared:  0.0003155 
## F-statistic: 1.473 on 1 and 1498 DF,  p-value: 0.225
coef p r.sq
bc -0.4496172 0.0003547 0.0574775
brt 0.5811577 0.0033410 0.0444243
dm -0.9740110 0.0000001 0.1236222
gam 0.2266407 0.0802197 0.0141012
glm 0.8607120 0.0000001 0.1277345
mx 0.5665322 0.0023231 0.0421256
rf 0.4820472 0.0001364 0.0652908




Relationship between test AUC and Pearson correlation, continental scale

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat at a continental scale, where model transferability is an issue. The lack of correlation indicates that test AUC is not a good predictor of model transferability. In fact the (not statistically significant) effect of test AUC on model accuracy is in fact negative.

## 
## Call:
## lm(formula = cor.all.pearson ~ test.auc, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.08294 -0.23876  0.03881  0.26916  0.68526 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.18543    0.05178   3.581 0.000353 ***
## test.auc     0.14329    0.07277   1.969 0.049143 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3471 on 1498 degrees of freedom
## Multiple R-squared:  0.002581,   Adjusted R-squared:  0.001915 
## F-statistic: 3.877 on 1 and 1498 DF,  p-value: 0.04914
coef p r.sq
bc -0.0085402 0.9184805 0.0000486
brt 1.0474117 0.0000032 0.1082652
dm 0.0633838 0.6358505 0.0010399
gam 0.4399592 0.0052959 0.0354378
glm 0.1741865 0.3406124 0.0042052
mx 0.8299756 0.0000081 0.0882975
rf 1.0407301 0.0000007 0.1084301




Relationship between test max TSS and Pearson correlation

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of the True Skill Statistic. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of TSS), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.pearson ~ test.max.tss, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.97760 -0.19729 -0.00948  0.19586  0.68878 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.18353    0.01774  10.348   <2e-16 ***
## test.max.tss  0.02749    0.03932   0.699    0.485    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2833 on 1498 degrees of freedom
## Multiple R-squared:  0.0003261,  Adjusted R-squared:  -0.0003412 
## F-statistic: 0.4887 on 1 and 1498 DF,  p-value: 0.4846
coef p r.sq
bc -0.2724049 0.0010347 0.0487230
brt 0.3681599 0.0027219 0.0463077
dm -0.7919089 0.0000000 0.1451834
gam 0.1051196 0.1994026 0.0076124
glm 0.5233680 0.0000004 0.1117083
mx 0.2780794 0.0167666 0.0261965
rf 0.2790858 0.0012865 0.0469444

## 
## Call:
## lm(formula = cor.all.pearson ~ test.max.tss, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.08369 -0.23715  0.03949  0.26910  0.68713 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.25120    0.02173  11.558   <2e-16 ***
## test.max.tss  0.08429    0.04818   1.749   0.0804 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3472 on 1498 degrees of freedom
## Multiple R-squared:  0.002039,   Adjusted R-squared:  0.001373 
## F-statistic: 3.061 on 1 and 1498 DF,  p-value: 0.08042
coef p r.sq
bc -0.0013853 0.9798725 0.0000030
brt 0.6207496 0.0000090 0.0987721
dm 0.0023480 0.9813519 0.0000025
gam 0.2893433 0.0036456 0.0384628
glm 0.1328092 0.2636155 0.0057821
mx 0.4748551 0.0000436 0.0746016
rf 0.6537736 0.0000052 0.0917834




Relationship between test max kappa and Pearson correlation

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of Cohen’s kappa. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of kappa), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.pearson ~ test.max.kappa, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.0136 -0.1864 -0.0110  0.1875  0.6778 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.23951    0.01544  15.511  < 2e-16 ***
## test.max.kappa -0.16304    0.04967  -3.282  0.00105 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2824 on 1498 degrees of freedom
## Multiple R-squared:  0.007141,   Adjusted R-squared:  0.006478 
## F-statistic: 10.77 on 1 and 1498 DF,  p-value: 0.001053
coef p r.sq
bc -0.5215903 0.0000121 0.0850502
brt 0.1560224 0.3353999 0.0048848
dm -1.0702771 0.0000000 0.1423376
gam 0.1256522 0.2601094 0.0058675
glm 0.5350059 0.0000967 0.0681048
mx 0.2842799 0.0755591 0.0145470
rf 0.0013232 0.9902915 0.0000007

## 
## Call:
## lm(formula = cor.all.pearson ~ test.max.kappa, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.04435 -0.23276  0.04383  0.26808  0.69290 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.35174    0.01891  18.603  < 2e-16 ***
## test.max.kappa -0.24047    0.06082  -3.954 8.05e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3458 on 1498 degrees of freedom
## Multiple R-squared:  0.01033,    Adjusted R-squared:  0.009668 
## F-statistic: 15.63 on 1 and 1498 DF,  p-value: 8.048e-05
coef p r.sq
bc -0.0801116 0.3135064 0.0047028
brt 0.4451316 0.0165916 0.0298310
dm -0.0222049 0.8713460 0.0001217
gam 0.3041199 0.0253858 0.0229227
glm 0.0687192 0.6590125 0.0009032
mx 0.3938497 0.0146502 0.0272687
rf 0.1765070 0.3321054 0.0043555




Relationship between bias strength and Pearson correlation, training region only

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.pearson ~ bias.strength, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9990 -0.2000 -0.0097  0.1912  0.6979 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.21211    0.01368  15.505   <2e-16 ***
## bias.strength -0.03438    0.02300  -1.494    0.135    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2832 on 1498 degrees of freedom
## Multiple R-squared:  0.001489,   Adjusted R-squared:  0.000822 
## F-statistic: 2.233 on 1 and 1498 DF,  p-value: 0.1353
coef p r.sq
bc -0.0114325 0.8131033 0.0002593
brt -0.0946265 0.1524139 0.0107487
dm 0.0327743 0.6618098 0.0008875
gam -0.0837514 0.0773772 0.0143697
glm -0.0535361 0.3715322 0.0036986
mx -0.0253557 0.7059572 0.0006603
rf -0.0152734 0.7313223 0.0005470




Relationship between proportion of suitable habitat that falls within species range and Pearson correlation, training region only

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.pearson ~ occupancy, data = new.table[new.table$method != 
##     "rf", ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.01089 -0.19977  0.00358  0.20865  0.67537 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.23432    0.02207  10.615   <2e-16 ***
## occupancy   -0.02734    0.03725  -0.734    0.463    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2873 on 1280 degrees of freedom
## Multiple R-squared:  0.0004206,  Adjusted R-squared:  -0.0003603 
## F-statistic: 0.5387 on 1 and 1280 DF,  p-value: 0.4631
coef p r.sq
bc -0.0227440 0.7510674 0.0004669
brt 0.0896229 0.3467935 0.0046601
dm -0.1411295 0.2032210 0.0074849
gam 0.0579195 0.4114168 0.0031260
glm -0.0541089 0.5426437 0.0017185
mx -0.0880597 0.3764948 0.0036227
rf -0.0185354 0.7786934 0.0003664




correlation vs. bias strength and proportion of suitable habitat within range, training region only

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.native.pearson ~ bias.strength * occupancy, 
##     data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.00637 -0.18912 -0.01297  0.19248  0.71104 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              0.32615    0.03739   8.723  < 2e-16 ***
## bias.strength           -0.23330    0.06292  -3.708 0.000217 ***
## occupancy               -0.20871    0.06360  -3.282 0.001056 ** 
## bias.strength:occupancy  0.36454    0.10737   3.395 0.000704 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2822 on 1496 degrees of freedom
## Multiple R-squared:  0.009508,   Adjusted R-squared:  0.007522 
## F-statistic: 4.787 on 3 and 1496 DF,  p-value: 0.002527





Relationship between bias strength and Pearson correlation, continental scale

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.pearson ~ bias.strength, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.02565 -0.23320  0.04329  0.26548  0.66652 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.33504    0.01672  20.035  < 2e-16 ***
## bias.strength -0.09789    0.02812  -3.481 0.000514 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3462 on 1498 degrees of freedom
## Multiple R-squared:  0.008024,   Adjusted R-squared:  0.007362 
## F-statistic: 12.12 on 1 and 1498 DF,  p-value: 0.0005139
coef p r.sq
bc -0.0217736 0.4903746 0.0022050
brt -0.1420215 0.0623347 0.0181661
dm -0.0123854 0.8158145 0.0002517
gam -0.1051944 0.0700029 0.0151186
glm -0.1401855 0.0351386 0.0203852
mx -0.1573131 0.0199420 0.0248232
rf -0.1100824 0.1386688 0.0101232




Relationship between proportion of suitable habitat that falls within species range and Pearson correlation, continental scale

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.pearson ~ occupancy, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.06854 -0.23424  0.04382  0.26361  0.68340 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.25078    0.02469  10.159   <2e-16 ***
## occupancy    0.06351    0.04167   1.524    0.128    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3473 on 1498 degrees of freedom
## Multiple R-squared:  0.001548,   Adjusted R-squared:  0.0008819 
## F-statistic: 2.323 on 1 and 1498 DF,  p-value: 0.1277
coef p r.sq
bc 0.1346311 0.0036988 0.0383451
brt 0.1904944 0.0823843 0.0157958
dm -0.1354503 0.0847317 0.0136952
gam 0.2245293 0.0088175 0.0313287
glm 0.1476488 0.1355217 0.0102858
mx -0.0313368 0.7559816 0.0004480
rf -0.0791234 0.4737358 0.0023788




correlation vs. bias strength and proportion of suitable habitat within range, continental scale

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.all.pearson ~ bias.strength * occupancy, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.01252 -0.23014  0.04414  0.26688  0.68483 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              0.34721    0.04583   7.576 6.22e-14 ***
## bias.strength           -0.19213    0.07712  -2.491   0.0128 *  
## occupancy               -0.02304    0.07796  -0.296   0.7676    
## bias.strength:occupancy  0.17268    0.13161   1.312   0.1897    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3459 on 1496 degrees of freedom
## Multiple R-squared:  0.01071,    Adjusted R-squared:  0.008729 
## F-statistic:   5.4 on 3 and 1496 DF,  p-value: 0.001072





Relationship between Pearson correlation and size of the species’ range, training region only

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.pearson ~ true.breadth, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.81004 -0.18476 -0.00645  0.18716  0.81975 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3.083e-01  1.063e-02   29.01   <2e-16 ***
## true.breadth -1.421e-05  1.014e-06  -14.01   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2665 on 1498 degrees of freedom
## Multiple R-squared:  0.1158, Adjusted R-squared:  0.1152 
## F-statistic: 196.2 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -5.80e-06 0.0096821 0.0305780
brt -3.02e-05 0.0000000 0.4364260
dm 1.04e-05 0.0026164 0.0411582
gam -1.42e-05 0.0000000 0.1907516
glm -2.24e-05 0.0000000 0.3002031
mx -2.43e-05 0.0000000 0.2806976
rf -1.62e-05 0.0000000 0.2856447




Relationship between Pearson correlation and size of the species’ range, continental scale

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.pearson ~ true.breadth, data = new.table)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.00513 -0.20291  0.03053  0.24568  0.78587 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   4.234e-01  1.305e-02   32.44   <2e-16 ***
## true.breadth -1.722e-05  1.246e-06  -13.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3273 on 1498 degrees of freedom
## Multiple R-squared:  0.1132, Adjusted R-squared:  0.1126 
## F-statistic: 191.2 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -1.10e-05 0.0000000 0.2624811
brt -3.58e-05 0.0000000 0.4618756
dm -5.70e-06 0.0207683 0.0245027
gam -1.40e-05 0.0000001 0.1236380
glm -9.50e-06 0.0019041 0.0437457
mx -2.77e-05 0.0000000 0.3560798
rf -2.15e-05 0.0000000 0.1781500




Relationship between test AUC and Hosmer-Lemeshow chisq statistic, training region only

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat within the training region. The lack of correlation indicates that test AUC is not a good predictor of the model’s ability to estimate the relative suitability of habitat, which is very problematic.

## 
## Call:
## lm(formula = cor.native.hoslem ~ test.auc, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -229813  -65445  -27183   21758  898869 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   383298      18921   20.26   <2e-16 ***
## test.auc     -443280      26593  -16.67   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 126800 on 1498 degrees of freedom
## Multiple R-squared:  0.1565, Adjusted R-squared:  0.1559 
## F-statistic: 277.8 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -555753.6 0.00e+00 0.1801005
brt -562572.8 0.00e+00 0.2078845
dm -187793.3 5.94e-05 0.0720774
gam -724177.7 0.00e+00 0.2834255
glm -714352.3 0.00e+00 0.2703855
mx -333254.0 0.00e+00 0.2196371
rf -609416.2 0.00e+00 0.1856885




Relationship between test AUC and Hosmer-Lemeshow chisq statistic, continental scale

This plot depicts the relationship between AUC on randomly withheld test data and the ability of the model to estimate the relative suitability of habitat at a continental scale, where model transferability is an issue. The lack of correlation indicates that test AUC is not a good predictor of model transferability. In fact the (not statistically significant) effect of test AUC on model accuracy is in fact negative.

## 
## Call:
## lm(formula = cor.all.hoslem ~ test.auc, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -349348 -130605  -70046   35265 2159369 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   600271      36408   16.49   <2e-16 ***
## test.auc     -640151      51170  -12.51   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 244100 on 1498 degrees of freedom
## Multiple R-squared:  0.09459,    Adjusted R-squared:  0.09399 
## F-statistic: 156.5 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -1022316.5 0.0000000 0.1842720
brt -1028457.4 0.0000000 0.1948595
dm -388839.4 0.0000000 0.1369762
gam -963178.6 0.0000002 0.1200715
glm -556069.2 0.0022033 0.0425569
mx -543511.9 0.0000000 0.2359828
rf -891803.3 0.0000000 0.1605362




Relationship between test max TSS and Hosmer-Lemeshow chisq statistic

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of the True Skill Statistic. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of TSS), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.hoslem ~ test.max.tss, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -172590  -69373  -32072   21435  918721 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    182482       8065   22.63   <2e-16 ***
## test.max.tss  -267228      17878  -14.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 128800 on 1498 degrees of freedom
## Multiple R-squared:  0.1298, Adjusted R-squared:  0.1292 
## F-statistic: 223.4 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -343949.4 0.0000000 0.1593058
brt -343336.5 0.0000000 0.2011186
dm -122497.8 0.0005113 0.0544870
gam -423015.7 0.0000000 0.2426798
glm -422072.6 0.0000000 0.2232601
mx -190652.5 0.0000000 0.1855444
rf -304741.0 0.0000020 0.0995989

## 
## Call:
## lm(formula = cor.all.hoslem ~ test.max.tss, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -300905 -137759  -72306   32205 2165365 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    313075      15390   20.34   <2e-16 ***
## test.max.tss  -392738      34117  -11.51   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 245900 on 1498 degrees of freedom
## Multiple R-squared:  0.08127,    Adjusted R-squared:  0.08066 
## F-statistic: 132.5 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -646036.8 0.0000000 0.1699399
brt -614904.3 0.0000000 0.1809304
dm -275202.1 0.0000001 0.1219005
gam -592133.4 0.0000003 0.1138773
glm -316043.2 0.0076080 0.0325150
mx -314118.8 0.0000000 0.2034503
rf -446162.4 0.0000105 0.0861900




Relationship between test max kappa and Hosmer-Lemeshow chisq statistic

These plots and models are similar to those for AUC above, but are instead calculated using the maximum value of Cohen’s kappa. The models are NOT thresholded for this comparision (which would typically be done at the threshold value corresponding to the max value of kappa), rather the max value is used as a quality indicator for the continuous model.

## 
## Call:
## lm(formula = cor.native.hoslem ~ test.max.kappa, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -130398  -68177  -42884   12078  975609 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      131782       7351  17.927   <2e-16 ***
## test.max.kappa  -215716      23645  -9.123   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 134400 on 1498 degrees of freedom
## Multiple R-squared:  0.05264,    Adjusted R-squared:  0.052 
## F-statistic: 83.23 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc -429438.01 0.0000002 0.1182377
brt -321058.76 0.0000055 0.1032930
dm -148198.04 0.0021375 0.0428038
gam -451882.38 0.0000000 0.1493941
glm -421424.33 0.0000000 0.1298571
mx -214534.20 0.0000001 0.1248340
rf -61657.82 0.4491484 0.0026545

## 
## Call:
## lm(formula = cor.all.hoslem ~ test.max.kappa, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -226072 -142042  -96837   30953 2117115 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      229802      13839  16.606  < 2e-16 ***
## test.max.kappa  -285062      44513  -6.404 2.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 253100 on 1498 degrees of freedom
## Multiple R-squared:  0.02665,    Adjusted R-squared:  0.026 
## F-statistic: 41.01 on 1 and 1498 DF,  p-value: 2.021e-10
coef p r.sq
bc -831583.746 0.0000000 0.1340618
brt -543015.805 0.0000515 0.0828726
dm -323652.119 0.0000061 0.0904940
gam -591601.771 0.0002217 0.0613224
glm -143671.576 0.3575461 0.0039203
mx -337743.066 0.0000001 0.1249741
rf -9263.028 0.9424451 0.0000242




Relationship between bias strength and Hosmer-Lemeshow chisq statistic, training region only

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.hoslem ~ bias.strength, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
##  -74735  -69682  -56990     562 1009818 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      74760       6672  11.206   <2e-16 ***
## bias.strength    -4166      11219  -0.371     0.71    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 138100 on 1498 degrees of freedom
## Multiple R-squared:  9.206e-05,  Adjusted R-squared:  -0.0005754 
## F-statistic: 0.1379 on 1 and 1498 DF,  p-value: 0.7104
coef p r.sq
bc -8439.211 0.8026380 0.0002898
brt 15752.094 0.5953402 0.0014874
dm -3512.234 0.8527511 0.0001599
gam -7359.283 0.8282318 0.0002184
glm -3664.729 0.9146825 0.0000533
mx -4219.059 0.8074861 0.0002755
rf -15038.462 0.6519629 0.0009436




Relationship between proportion of suitable habitat that falls within species range and Hosmer-Lemeshow chisq statistic, training region only

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.hoslem ~ occupancy, data = new.table[new.table$method != 
##     "rf", ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -101030  -64282  -48177    7053  982955 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    31830      10292   3.093  0.00203 ** 
## occupancy      69376      17368   3.995 6.85e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 133900 on 1280 degrees of freedom
## Multiple R-squared:  0.01231,    Adjusted R-squared:  0.01154 
## F-statistic: 15.96 on 1 and 1280 DF,  p-value: 6.85e-05
coef p r.sq
bc 47316.64 0.3441459 0.0041442
brt -16086.92 0.7061654 0.0007498
dm 160550.74 0.0000000 0.1519308
gam 65448.95 0.1922770 0.0078579
glm 66925.53 0.1861099 0.0080792
mx 87840.77 0.0005220 0.0543163
rf 77193.47 0.1174627 0.0113083




chisq statistic vs. bias strength and proportion of suitable habitat within range, training region only

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.native.hoslem ~ bias.strength * occupancy, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -150366  -66898  -46529    5741  936242 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               -27132      18080  -1.501    0.134    
## bias.strength             121452      30423   3.992 6.87e-05 ***
## occupancy                 185929      30753   6.046 1.87e-09 ***
## bias.strength:occupancy  -230224      51918  -4.434 9.91e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 136500 on 1496 degrees of freedom
## Multiple R-squared:  0.02499,    Adjusted R-squared:  0.02303 
## F-statistic: 12.78 on 3 and 1496 DF,  p-value: 3.011e-08





Relationship between bias strength and Hosmer-Lemeshow chisq statistic, continental scale

This plot and model examine the relationship between the strength of spatial sampling bias and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.hoslem ~ bias.strength, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -152408 -146005 -116887   26984 2095217 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     150640      12391  12.157   <2e-16 ***
## bias.strength     2070      20837   0.099    0.921    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 256500 on 1498 degrees of freedom
## Multiple R-squared:  6.587e-06,  Adjusted R-squared:  -0.000661 
## F-statistic: 0.009868 on 1 and 1498 DF,  p-value: 0.9209
coef p r.sq
bc -1627.309 0.9788592 0.0000033
brt 33936.683 0.5444807 0.0019364
dm -3128.317 0.9123579 0.0000562
gam -16553.045 0.8112388 0.0002646
glm -7719.950 0.9084281 0.0000614
mx 20779.668 0.4453391 0.0026993
rf -5024.458 0.9237366 0.0000425




Relationship between proportion of suitable habitat that falls within species range and Hosmer-Lemeshow chisq statistic, continental scale

This plot and model examine the relationship between the proportion of suitable habitat continent-wide that is within the species range and the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.hoslem ~ occupancy, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -188991 -143326 -108166   23138 2061779 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   199672      18184  10.980  < 2e-16 ***
## occupancy     -86942      30693  -2.833  0.00468 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 255800 on 1498 degrees of freedom
## Multiple R-squared:  0.005328,   Adjusted R-squared:  0.004664 
## F-statistic: 8.024 on 1 and 1498 DF,  p-value: 0.004678
coef p r.sq
bc -98876.92 0.2768610 0.0054719
brt -135278.23 0.0919920 0.0148706
dm 80632.97 0.0546697 0.0169868
gam -244757.04 0.0165119 0.0263179
glm -177949.76 0.0726879 0.0148366
mx 18309.53 0.6503011 0.0009532
rf -52241.19 0.5018279 0.0020909




chisq statistic vs. bias strength and proportion of suitable habitat within range, continental scale

Combining the two above into a single 3D plot and joint model with interactions.

## 
## Call:
## lm(formula = cor.all.hoslem ~ bias.strength * occupancy, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -233916 -143984 -103141   22504 2099400 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               144142      33868   4.256 2.21e-05 ***
## bias.strength             110750      56990   1.943   0.0522 .  
## occupancy                  12906      57609   0.224   0.8228    
## bias.strength:occupancy  -199131      97256  -2.047   0.0408 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 255600 on 1496 degrees of freedom
## Multiple R-squared:  0.008114,   Adjusted R-squared:  0.006125 
## F-statistic: 4.079 on 3 and 1496 DF,  p-value: 0.006752





Relationship between Hosmer-Lemeshow chisq statistic and size of the species’ range, training region only

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat within the training region.

## 
## Call:
## lm(formula = cor.native.hoslem ~ true.breadth, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -215254  -40981    -327   16947  837881 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -3.163e+04  4.222e+03  -7.493 1.15e-13 ***
## true.breadth  1.306e+01  4.029e-01  32.417  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 105900 on 1498 degrees of freedom
## Multiple R-squared:  0.4123, Adjusted R-squared:  0.4119 
## F-statistic:  1051 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 17.057814 0.0000000 0.5481931
brt 15.478361 0.0000000 0.5743689
dm 2.772286 0.0014253 0.0461079
gam 16.697841 0.0000000 0.5205979
glm 16.807351 0.0000000 0.5186342
mx 7.024738 0.0000000 0.3535705
rf 16.244829 0.0000000 0.5097342




Relationship between Hosmer-Lemeshow chisq statistic and size of the species’ range, continental scale

This plot and model examine whether the size of the species’ range affects the ability to infer the relative suitability of habitat when models are transferred to the continental scale.

## 
## Call:
## lm(formula = cor.all.hoslem ~ true.breadth, data = new.table)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -389345  -82611  -27523   10720 2204686 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -2.819e+04  8.212e+03  -3.433 0.000614 ***
## true.breadth  2.253e+01  7.837e-01  28.743  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 205900 on 1498 degrees of freedom
## Multiple R-squared:  0.3555, Adjusted R-squared:  0.355 
## F-statistic: 826.2 on 1 and 1498 DF,  p-value: < 2.2e-16
coef p r.sq
bc 34.49508 0 0.6778589
brt 29.74779 0 0.5950245
dm 10.42267 0 0.2888838
gam 25.07462 0 0.2811433
glm 19.48804 0 0.1811145
mx 13.18943 0 0.5034718
rf 26.81190 0 0.5605916